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Question

In the figure below, ray OS stands on a line POQ. Ray OR and ray OT are angle bisectors of POS and SOQ, respectively. If POS = x, find ROT.


A

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B

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C

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D

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Solution

The correct option is B


Ray OS stands on the line POQ, so that,

POS + SOQ = 180

But, POS = x

Hence, x+ SOQ = 180

SOQ = 180x

Now, ray OR bisects POS.

Hence, ROS = 12 × POS = 12 × x = x2

Similarly, SOT =12 × SOQ = 12 × ( 180 - x) = 90x2

ROT = ROS + SOT = x2 + 90x2 = 90


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